Begin by separating the egg yolk from the white and placing the yolk in a bowl.
Add the mustard, salt, pepper, and vinegar to the bowl and whisk the ingredients together until they are well combined.
Start adding the oil very slowly, drop by drop, while continuously whisking the mixture.
As the mixture begins to emulsify, gradually increase the flow of oil while continuing to whisk.
Keep whisking until the mayonnaise reaches a thick consistency.
If you like, mix in a tablespoon of sesame oil for extra flavor.
Taste and adjust the seasoning if necessary, then serve or store the mayonnaise.
